Score : $700$ points

Problem Statement

Given is a sequence $p$ of length $N+M$, which is a permutation of $(1,2 \ldots, N+M)$. The $i$-th term of $p$ is $p_i$.

You can do the following Operation any number of times.

Operation: Choose an integer $n$ between $1$ and $N$ (inclusive), and an integer $m$ between $1$ and $M$ (inclusive). Then, swap $p_{n}$ and $p_{N+m}$.

Find the minimum number of Operations needed to sort $p$ in ascending order. We can prove that it is possible to sort $p$ in ascending order under the Constraints of this problem.

Constraints

• All values in input are integers.
• $1 \leq N,M \leq 10^5$
• $1 \leq p_i \leq N+M$
• $p$ is a permutation of $(1,2 \ldots, N+M)$.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$p_{1}$ $\cdots$ $p_{N+M}$

Output

Print the minimum number of Operations needed to sort $p$ in ascending order.

2 3
1 4 2 5 3

3

5 7
9 7 12 6 1 11 2 10 3 8 4 5

10